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The phrase "a simple explanation is given" is correct and usable in written English.
It can be used when indicating that a straightforward clarification or description has been provided.
Example: "In the following section, a simple explanation is given to help clarify the complex concepts discussed earlier."
Alternatives: "a straightforward explanation is provided" or "a clear explanation is offered".
Exact(1)
A simple explanation is given for the required rank deficiency of the equilibrium matrix that leads to a non-degenerate structure.
Similar(59)
A simple explanation is that bare linguistic competence gives us knowledge that are no such thresholds.
A simple explanation is usually best.
A simple explanation of the phenomenon is given in a frame of the gradient-curvature drift model.
Dr. Marshall used to ask his residents if they had learned about Occam's razor: Given the choice between multiple explanations for any given phenomenon, the simplest explanation is almost always right.
The simpler explanation is that this is merely Trump never being willing to give an inch.
The simplest explanation is true.
The simplest explanation is jobs.
One simple explanation to this was given by Campbell [43] who reformulated an original idea by Guilford [44] into a theory of "blind variation and selective attention".
A step by step explanation shall be given using the simple scenario in Figure 1.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com